Question

A system of equations is shown below:

5x - 5y = 10
3x - 2y = 2

Part A: Create an equivalent system of equations by replacing one equation with the sum of that equation and a multiple of the other. Show the steps to do this.

Part B: Show that the equivalent system has the same solution as the original system of equations.

Answer 1

@phi @Hero

Answer 2

multiply the first equation by 1/2, then add the result to the second equation.

Answer 3

Should i multiply 1/2 by 10
Then add the five to 2?

Answer 4

Multiply the first equation by 1/2. In other words, divide both sides of the first equation by 2

Answer 5

ok i think i get it

Answer 6

but that just part A correct

Answer 7

\[2.5x-2.5y=10 + 3x - 2y= 2\]

Answer 8

that would equal 5.5x-4.5y=12

Answer 9

er no the 10 should be a 5 so 5.5x+4.5y=7

Answer 10

Actually, what I meant to say was multiply both sides of the first equation by 1/5

You shouldn't end up with decimals if you do that.

Answer 11

You should try to avoid decimals at all costs.

Answer 12

1x-1y=2
+3x-2y=2

Answer 13

4x-3y=4

Answer 14

right?

Answer 15

Yes, correct. So what would be the equivalent system now?

Answer 16

4x-3y=4?

Answer 17

That's not a system. That's just an equation.